The power-series and hypergeometric-function expansions
are both given by one-sided
infinite series (\(n\ge 0\) ) whose coefficients obey three-term recurrence relations.
This fact requires a free parameter
which posteriorly must be computed from a “characteristic" equation
which assures
non trivial solutions for the
recurrence relations. The absence of free parameters
would demand two-sided infinite series (\(-\infty <n<+\infty \) ) as in the case
of Mathieu equation [1]}.
